Abstract
Wheeler’s delayedchoice experiment illustrates vividly that the observer plays a central role in quantum physics by demonstrating that complementarity or wave–particle duality can be enforced even after the photon has already entered the interferometer. The delayedchoice quantum eraser experiment further demonstrates that complementarity can be enforced even after detection of a quantum system, elucidating the foundational nature of complementarity in quantum physics. However, the applicability of the delayedchoice method for practical quantum information protocols continues to be an open question. Here, we introduce and experimentally demonstrate the delayedchoice decoherence suppression protocol, in which the decision to suppress decoherence on an entangled twoqubit state is delayed until after the decoherence and even after the detection of a qubit. Our result suggests a new way to tackle Markovian decoherence in a delayed manner, applicable for practical entanglement distribution over a dissipative channel.
Introduction
Complementarity normally refers to the wave–particle dual nature in quantum physics. In the delayedchoice experiment proposed by Wheeler, the choice to observe the wave or particle nature is delayed until after the quantum system has already entered the interferometer^{1,2}. It is even possible to delay the choice after detection of the quantum system by using an ancilla entangled with the quantum system^{3,4,5,6}. For example, a delayedchoice quantum eraser is proposed and demonstrated, where the decision of whether to read out or erase the whichpath information can be delayed till after the registration of the quanta^{3,4}. Recently, experiments to investigate the intermediate behaviour between wave and particle nature have been proposed and demonstrated^{5,6,7}. It is also recently shown that entanglement swapping, quantum walk and uncertainty principle can be demonstrated using delayedchoice method^{8,9,10,11,12}. Although the fundamental aspects of delayedchoice experiments have been well studied, practicality of the delayedchoice method was rather obscure.
An intriguing question may arise as to whether the concept of delayedchoice can be adopted for quantum information protocols such as suppressing decoherence, which is a central problem in emerging quantum technology^{13,14,15}. This is a particularly interesting question for Markovian decoherence. Markovian decoherence is considered to be difficult to tackle once the decoherence takes place, since a posteriori methods such as rephasing^{16,17} or dynamical decoupling^{18,19} cannot be used.
In this Article, we propose and experimentally demonstrate a delayedchoice decoherence suppression scheme by using photonic polarization qubits. In contrast to the normal decoherence suppression scheme^{20,21,22,23}, in which the choice whether or not to suppress decoherence is naturally made before the decoherence by the initial weak measurement (WM), our decoherence suppression scheme delays the choice after the decoherence itself. We demonstrate that although the choice to suppress decoherence is made by delayed WM after the decoherence and even after detection of the quantum system, our scheme can suppress decoherence successfully.
Results
Schematic and theory
The delayedchoice decoherence suppression scenario is schematically shown in Fig. 1a. A twoqubit entangled state, , is prepared at the time t=0 and sent to Alice and Bob with temporal delays and , respectively. At time t_{D}, Bob’s qubit suffers from Markovian amplitude damping decoherence^{15}, which is described by a quantum map: , where D is the magnitude of amplitude damping, and subscript S (E) refers to system (environment). As a result, the twoqubit state becomes mixed, causing reduced entanglement quantified by concurrence, C_{d}
Bob’s reversing measurement (RM), applied immediately after the decoherence, is represented as , where and p_{r} is strength of the RM. Alice’s decision at time t_{W} whether to suppress the decoherence, by applying the WM on her qubit, may be made after the decoherence (t_{W}>t_{D}) or even after the detection of Bob’s qubit (t_{W}>t_{B}). Alice’s WM is represented as , where and p is WM strength. The reversing measurement strength is chosen to be p_{r}=p+D(1−p) (refs 20, 21, 23). After Alice’s WM and Bob’s RM, entanglement in the twoqubit is quantified by concurrence C_{r} (H.T.L., J.C.L., K.H.H. and Y.H.K., manuscript in preparation),
Note that C_{r}>C_{d} that indicates that the delayedchoice decoherence suppression scheme can successfully circumvent Markovian amplitude damping decoherence. It is worth pointing out that, since the WM and RM are both nonunitary, the success probability of our scheme is less than unity. The success probability of the delayedchoice decoherence suppression scheme is (refs 21, 23).
Experimental implementation
The experimental schematic of delayedchoice decoherence suppression is shown in Fig. 1b. The qubit is encoded in a polarization state of a singlephoton: 0›≡H›, 1›≡V›, where H› is horizontal polarization and V› is vertical polarization. The initial twoqubit entangled state (Φ› with ) is prepared by using typeI spontaneous parametric down conversion from a 6mm thick βBaB_{2}O_{4} crystal^{24}. The photons are frequency filtered by a set of interference filters with 5 nm bandwidth. Optical delays and are implemented with singlemode fibres (SMF). Note that wave plates are used to compensate polarization rotation by SMFs at each SMF output. The Markovian amplitude damping decoherence (D) is set up with a displaced Sagnac interferometer^{21,23}. The WM and the RM are implemented with wave plates and Brewster’s angle glass plates^{25}. The final twoqubit state is analysed with wave plates and polarizers via twoqubit quantum state tomography^{23}.
We implement the delayedchoice decoherence suppression scheme in two configurations, spacelike separation and timelike separation, by varying the temporal delays and . The space–time diagrams for the two configurations are shown in Fig. 2. First, in Fig. 2a, we set up the temporal delays such that Alice’s WM and Bob’s decoherence events are in spacelike separation. To make sure that the delayedchoice is indeed made after the decoherence itself, we need to consider the timing resolution of the detector (0.35 ns), the coincidence time window for measuring the joint detection events (2.0 ns) and the physical dimensions of the apparatus implementing WM, RM and D. The times for the photon to traverse the apparatus implementing WM, RM and D are 0.10, 0.33 and 1.0 ns, respectively. The overall timing uncertainty is thus 3.8 ns. Since Alice’s WM is made 5.3 ns after the decoherence event, it can be guaranteed that no information about Alice’s choice can be transferred to Bob at the time of decoherence. Furthermore, Alice’s WM and Bob’s decoherence are physically separated by L=2.8 m, so that the time difference between the two events is shorter than the time at which light travels between them (5.3 ns<L/c=9.3 ns). The two events are, thus, in spacelike separation as neither of the events are within the forward light cones of each other, see Fig. 2a. This ensures that no causal relationship, that is, no classical communication, can be established between the two events in this setting.
Second, we set up the apparatus such that Alice’s WM is in timelike future of the decoherence event on Bob, see Fig. 2b. Experimentally, we increase by inserting a 400m fibre spool on Alice’s side to achieve . As with the spacelike separation depicted in Fig. 2a, Alice’s WM is made sufficiently after the decoherence itself, hence no information about Alice’s choice can be sent back to Bob’s decoherence event. In the timelike separation, however, it is possible for Bob to send classical information about the decoherence to Alice, possibly affecting Alice’s WM.
Discussion
The delayedchoice decoherence suppression is demonstrated in Fig. 3. We first fixed the magnitude of decoherence to be D=0.617 and varied the WM strength p and monitored the concurrence of the final twoqubit state, see Fig. 3a. The concurrence increases as the WM strength increases. For both spacelike separation shown in Fig. 2a and timelike separation shown in Fig. 2b, the decoherence is successfully circumvented by using our delayedchoice decoherence suppression scheme. Then we set the WM strength at P=0.617 and observe the concurrence as D increases, see Fig. 3b. When the twoqubit system is subject to decoherence, entanglement of the system significantly degrades as D becomes large. However, when the delayedchoice decoherence suppression scheme is applied, more entanglement is shared by Alice and Bob, as evidenced in higher concurrences (C_{r}>C_{d}). This again confirms that it is indeed possible to perform delayedchoice decoherence suppression.
Our decoherence suppression scheme can be applicable to practical entanglement distribution scenarios, an example of which is shown in Fig. 4. First, Alice generates N identical pairs of entangled qubits and shares it with Bob through a quantum channel that has unknown amplitude damping decoherence in the channel, see Fig. 4a. The decoherence causes the twoqubit state to become a mixed state ρ_{d} and lowers concurrence. Alice and Bob store the qubits in quantum memories to use it on demand. Alice and Bob do not know the existence of decoherence in advance and the ensemble of quantum states shared by Alice and Bob is , see Fig. 4b. Bob then uses a small subset of his qubits to estimate the magnitude of decoherence D by monitoring the weight between 0›‹0 and 1›‹1. Assuming the initial state Φ› with , the quantum state of Bob’s qubit after decoherence is . As Bob makes m independent measurements, the variance of Bob’s estimation of D is . Bob then uses a classical communication channel to inform the measured D value to Alice. Now, Alice and Bob share N−m identical pairs of partially entangled qubits with known D, see Fig. 4c. The delayedchoice decoherence suppression scheme can be applied with a reversing measurement strength ρ_{r} (refs 20, 21, 23). As a result, the two parties now share highly entangled qubits, with concurrence C_{r}, while the final number of qubits is decreased to (N−m)P_{S} due to Bob’s estimation of D and success probability P_{S} of the scheme. Our delayedchoice decoherence suppression scheme provides a new strategy for entanglement distillation over a decoherence channel.
In summary, we have proposed and experimentally demonstrated the delayedchoice decoherence suppression in which the choice whether to suppress decoherence is made after the decoherence and even after the detection of a qubit. It is interesting to note that our delayedchoice decoherence suppression scheme allows to circumvent Markovian amplitude damping decoherence, even though the decision to suppress the decoherence made after the decoherence itself. While the demonstration in this paper utilized photonic polarization entanglement, the delayedchoice scheme demonstrated in this work can be generalized and applied to other quantum systems. Our result thus provides a new direction in tackling decoherence in a delayed manner and has important implications in practical implementations of various quantum information protocols.
Additional information
How to cite this article: Lee, J.C. et al. Experimental demonstration of delayedchoice decoherence suppression. Nat. Commun. 5:4522 doi: 10.1038/ncomms5522 (2014).
References
Wheeler J. A., Zurek W. H. (eds)Quantum Theory and Measurement Princeton University (1983).
Jacques, V. et al. Experimental realization of Wheeler’s delayedchoice gedanken experiment. Science 315, 966–968 (2007).
Kim, Y.H., Yu, R., Kulik, S. P., Shih, Y. & Scully, M. O. Delayed ‘choice’ quantum eraser. Phys. Rev. Lett. 84, 1–5 (2000).
Ma, X.S. et al. Quantum erasure with causally disconnected choice. Proc. Natl Acad. Sci. USA 110, 1221–1226 (2013).
Peruzzo, A., Shadbolt, P., Brunner, N., Popescu, S. & O’Brien, J. L. A quantum delayedchoice experiment. Science 338, 634–637 (2012).
Kaiser, F., Coudreau, T., Milman, P., Ostrowsky, D. B. & Tanzilli, S. Entanglementenabled delayedchoice experiment. Science 338, 637–640 (2012).
Ionicioiu, R. & Terno, D. R. Proposal for a quantum delayedchoice experiment. Phys. Rev. Lett. 107, 230406 (2011).
Ma, X.S. et al. Experimental delayedchoice entanglement swapping. Nat. Phys. 8, 479–484 (2012).
Jeong, Y.C., Di Franco, C., Lim, H.T., Kim, M. S. & Kim, Y.H. Experimental realization of a delayedchoice quantum walk. Nat. Commun. 4, 2471 (2013).
Berta, M., Christandl, M., Colbeck, R., Renes, J. M. & Renner, R. The uncertainty principle in the presence of quantum memory. Nat. Phys. 6, 659–662 (2010).
Li, C.F., Xu, J.S., Xu, X.Y., Li, K. & Guo, G.C. Experimental investigation of the entanglementassisted entropic uncertainty principle. Nat. Phys. 7, 752–756 (2011).
Prevedel, R., Hamel, D. R., Colbeck, R., Fisher, K. & Resch, K. J. Experimental investigation of the uncertainty principle in the presence of quantum memory and its application to witnessing entanglement. Nat. Phys. 7, 757–761 (2011).
Nielsen, M. & Chuang, I. Quantum Computation and Quantum Information Cambridge University Press (2000).
Zurek, W. H. Decoherence, einselection, and the quantum origins of the classical. Rev. Mod. Phys. 75, 715–775 (2003).
Almeida, M. P. et al. Environmentinduced sudden death of entanglement. Science 316, 579–582 (2007).
Xu, J.S. et al. Measurementinduced quantum coherence recovery. New J. Phys. 11, 043010 (2009).
Xu, X.Y., Xu, J.S., Li, C.F. & Guo, G.C. Measurementinduced quantum entanglement recovery. Phys. Rev. A 82, 022324 (2010).
Biercuk, M. J. et al. Optimized dynamical decoupling in a model quantum memory. Nature 458, 996–1000 (2009).
Du, J. et al. Preserving electron spin coherence in solids by optimal dynamical decoupling. Nature 461, 1265–1268 (2009).
Korotkov, A. N. & Keane, K. Decoherence suppression by quantum measurement reversal. Phys. Rev. A 81, 040103(R) (2010).
Lee, J.C., Jeong, Y.C., Kim, Y.S. & Kim, Y.H. Experimental demonstration of decoherence suppression via quantum measurement reversal. Opt. Express 19, 16309–16316 (2011).
Sun, Q., AlAmri, M., Davidovich, L. & Zubairy, M. S. Reversing entanglement change by a weak measurement. Phys. Rev. A 82, 052323 (2010).
Kim, Y.S., Lee, J.C., Kwon, O. & Kim, Y.H. Protecting entanglement from decoherence using weak measurement and quantum measurement reversal. Nat. Phys. 8, 117–120 (2012).
Shih, Y. H. & Alley, C. O. New type of EinsteinPodolskyRosenBohm experiment using pairs of light quanta produced by optical parametric down conversion. Phys. Rev. Lett. 61, 2921–2924 (1988).
Kim, Y.S., Cho, Y.W., Ra, Y.S. & Kim, Y.H. Reversing the weak quantum measurement for a photonic qubit. Opt. Express 17, 11978–11985 (2009).
Acknowledgements
This work was supported in part by the National Research Foundation of Korea (Grant No. 20110021452 and No. 2013R1A2A1A01006029). J.C.L. and H.T.L. acknowledge support from the National Junior Research Fellowship (Grant No. 2012000741 and 2012000642, respectively). Y.C.J. acknowledges support from BK21. M.S.K. acknowledges support from UK EPSRC. M.S.K. thanks M. Genoni for discussions.
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M.S.K. and Y.H.K. conceived the idea; J.C.L., H.T.L., and Y.H.K. further developed the idea and designed the experiment; J.C.L., H.T.L. and K.H.H. carried out the experiment with the help of Y.C.J. under the supervision of Y.H.K.; J.C.L., H.T.L., K.H.H. and Y.H.K. analysed the data; all authors discussed the results and contributed to writing the manuscript.
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Lee, JC., Lim, HT., Hong, KH. et al. Experimental demonstration of delayedchoice decoherence suppression. Nat Commun 5, 4522 (2014). https://doi.org/10.1038/ncomms5522
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DOI: https://doi.org/10.1038/ncomms5522
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